Question: $h(x) = -4x^{3}+3x^{2}-4(f(x))$ $f(t) = 3t+5$ $g(x) = 4x-2(f(x))$ $ g(f(-3)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(-3)$ . Then we'll know what to plug into the outer function. $f(-3) = (3)(-3)+5$ $f(-3) = -4$ Now we know that $f(-3) = -4$ . Let's solve for $g(f(-3))$ , which is $g(-4)$ $g(-4) = (4)(-4)-2(f(-4))$ To solve for the value of $g$ , we need to solve for the value of $f(-4)$ $f(-4) = (3)(-4)+5$ $f(-4) = -7$ That means $g(-4) = (4)(-4)+(-2)(-7)$ $g(-4) = -2$